High School SMILE Meeting
21 March 2006

Chris Etapa (Gunsalaus Academy)                       Information on a low-cost MSSE Program
is enrolled in a Master of Science in Science Education degree program at De Paul University. A new group will be admitted into that program, which is funded by the National Science Foundation.  For more information on the program see the following website: http://csh.depaul.edu/academics/graduate/stem-studies/Pages/default.aspx.  The degree program requires 12 courses, with 1 course per academic year  term, and 2 short courses in the summer. Thanks, Chris

Fred Schaal (Lane Tech HS, mathematics)               Graphing Inverse Trig Functions
noted that books don't tell how to graph inverse trig functions. Fred figured out a pretty good way to do it with a TI-83 calculator. He projected the Ti-83 screen on the wall for us to follow along with his method. He had written a little program to plot these functions. First Fred plotted the inverse sin and the plot looked reasonable. But the same method with the inverse cosine did not give a curve that made sense. Some adjustments were made in the graph scale, as suggested by the friendly crowd, and the inverse cosine curve looked better. Fred then tried the inverse tangent and it also looked reasonable. Interesting, Fred!

Fred Farnell (Lane Tech HS, physics)                       Kepler's Law Website
found The Planetary Orbital Simulation website, from The University of Nebraska, Lincoln http://astro.unl.edu/naap/pos/animations/kepler.swf. It  presents a nice simulation/explanation of various aspects of Kepler's Laws and simulations of the orbits of the planets. Fred had put together a nice exercise based on the simulator:


The first example was Mercury, and the simulation clearly showed the details of the elliptical orbit. We displayed vectors for its velocity and acceleration, which changed continuously as the planet traversed the orbit; the correlation of this property with the change in velocity of the planet as it gets further away and closer to the sun could be clearly simulated by adjusting the orbital parameters. Kepler's Second Law (equal areas in equal times) could also be simulated in a very useful way.

Porter Johnson pointed out that the planet Pluto moves about the sun with a period that is precisely 3/2 that of the planet Neptune. Furthermore, there are several objects that move with this same period. For details see the website The Plutinos: http://www2.ess.ucla.edu/~jewitt/kb/plutino.html.  In addition, the planet Mercury rotates with a period of 2/3 of its orbital period about the sun:  http://cseligman.com/text/planets/mercuryrot.htm.
This is a very nice teaching tool! Thanks, Fred.

Roy Coleman (Morgan Park HS, retired)                Software
called attention to the XnView website, http://www.xnview.com/, which contains free software for conversion of image files to various formats, such as JPEG, GIF, and TIF. Then he touted the Google Earth website, http://earth.google.com/, which contains free downloadable software of graphical images of the earth, with the capability of magnification and localization.
Neat! Thanks, Roy.

Larry Alofs (Kenwood HS, retired)             Piezoelectricity
first showed us a little piezoelectric igniter, like those used in gas grills. Larry then showed us another version of the igniter (the "matchless pilot light"), and a third example (a cigarette lighter; it would also need butane as a fuel to ignite and burn). Each uses a crystal (of something Larry couldn't remember) which is encapsulated and can be squeezed at either end. Larry took the lighter apart for us, projecting the (small) parts on the screen using the overhead projector. A tiny hammer mechanism hits the crystal and causes the spark.

Larry then showed, using a homemade electroscope apparatus, that the crystal from one of the igniters, when it is compressed, can transfer charge to another object. It was done by transferring charge to two small strips of aluminum foil which were hanging together, suspended from a paper clip, causing them to repel each other. The harder Larry compressed the crystal, the more charge was transferred and the greater the repelling of the two aluminum foil strips.

For additional information on Piezoelectricity see the Wikipedia website:  http://en.wikipedia.org/wiki/Piezoelectricity#Crystal_classes, from which the following has been excerpted:

"Many materials exhibit the effect, including quartz analogue crystals like berlinite, gallium orthophosphate, ceramics, tungsten, barium titanate, strontium titanate, lead zirconate titanate, lithium niobate, lithium tantalate, sodium tungstate, ... . Materials like rubber, wool, wood fiber, and silk often behave as electrets. Although this phenomenon is often confused with piezoelectricity, the two phenomena are distinct. The orientation of polarization in a piezoelectric is limited by the symmetry, whereas the polarization direction in an electret is not. The polymer polyvinylidene fluoride, PVDF exhibits piezoelectricity several times larger than quartz. Bone exhibits some piezoelectric properties, due to the apatite crystals: it has been hypothesized that this is part of the mechanism of bone remodeling in response to stress, as the electric fields on the apatite crystals stimulate further bone growth."
Quite amazing and put together from stuff around the house! Thanks, Larry. 

Ann Brandon (Joliet West, retired)                    Math Puzzle (Kakuro) and Paper Clip Energy
had us each take a paper clip and bend it into a triangle with one side of the triangle being formed from the two overlapping ends of the clip and held together by friction. When you drop it and the ends come apart, the potential energy stored in this configuration may be  released when it it hits the ground, and the triangle may jump back up. We didn't have a lot of success in our attempts to launch this device!

Ann then showed us two examples of a Kakuro puzzle, sort of like a crossword puzzle but with arithmetic sums (across and down) instead of words. You are not allowed to use the same numeral (1-9) in the same row or column of a given block.  Her puzzle was taken from the book Kakuto presented by New York Times puzzle editor Will Shortz --- one hundred addictive puzzles, St Martins Press 2006 (ISBN: 0-312r36042-8):  http://www.holtzbrinckpublishers.com/stmartins/search/SearchBookDisplay.asp?BookKey=4523318.  See also the book Kakuro for Dummieshttp://www.mcnallyrobinson.com/product.php?txtCatID=389&txtProdID=332997.  These puzzles can be quite difficult, since they cannot be completed one piece at a time!
Rather puzzling, Ann.

Bill Colson commented on the Mr Calm - Mr Angry optical illusion at the last meeting. Bill had gone to one of the web sites included in the newsletter. Bill said that the writer of one of the web sites explained that each image is overprinted with features at different resolutions, presumably features appearing and disappearing as you get closer to or farther away from the image.

Bill Shanks (Joliet Central, retired)                   Whistle Balloon Helicopter
Bill shared with us a favorite physics toy -- the Whistle Balloon Helicopter  http://www.costumes4less.com/products/kb125/Whistle_Balloon_Helicopter. It is also available as the Neato Balloon Helicopter.  It is great for illustrating Newton's Third Law. A balloon is inflated and attached to a little nozzle on a rotor with three blades. As the air comes out of the balloon, it causes the rotor to spin and you get a little helicopter that flies up. Look for it at toy stores or museum stores.
And off we go! Thanks, Bill.

Bud Schultz (Aurora Middle School)                        Leyden Jar
brought in a Van de Graaff generator [http://www.amasci.com/emotor/vdg.html] and a homemade capacitor -- a Leyden Jar made from a plastic soup container, aluminum foil, and a bit of wire. For details see the website  http://www.alaska.net/~natnkell/leyden.htmBud used the generator to charge the capacitor.  Next he disassembled the Leyden Jar, and gave the parts (aluminum foil, wife, plastic container) to Fred to examine.  He then put Leyden Jar back together and -- to our surprise -- it was still charged. Fred then discharged the capacitor through his finger.
Quite stimulating!  Thanks, Bud.

Our next SMILE meeting will be on Tuesday April 04, 2006. See you there!

Notes prepared by Ben Stark and Porter Johnson.